Capacitively-driven tunable coupling

ABSTRACT

A capacitively-driven tunable coupler includes a coupling capacitor connecting an open end of a quantum object (i.e., an end of the object that cannot have a DC path to a low-voltage rail, such as a ground node, without breaking the functionality of the object) to an RF SQUID having a Josephson element capable of providing variable inductance and therefore variable coupling to another quantum object.

GOVERNMENT INTEREST

The invention was made under Government Contract Number 30069353.Therefore, the US Government has rights to the invention as specified inthat contract.

TECHNICAL FIELD

The present invention relates generally to superconducting circuits, andspecifically to capacitively-driven tunable coupling of quantum objects.

BACKGROUND

Conventional microwave mechanical, electro-mechanical, and electronicswitches may not compatible with on-chip integration with, and cryogenicoperation of, superconducting electronic circuits, because ofincompatible fabrication processes and high power dissipation. Likewise,tunable filters that are commonly realized by use of either activecomponents such as voltage-variable capacitors (i.e., varactors),mechanical drivers, or ferroelectric and ferrite materials, are noteasily controllable by signal levels that can be generated with singleflux quantum (SFQ) technologies, and many are not operable at cryogenictemperatures. While superconducting microwave filters, both fixed andtunable, have been previously realized using both high temperature andlow temperature superconductors, their use in switching applicationssuffers from high return loss, limited usable bandwidth, and poorout-of-band off-state isolation.

In certain superconducting contexts, a coupler can be provided toexchange information between objects by turning on some coupling betweenthem, or to isolate the objects by turning off that coupling. A tunablecoupler is one that controls a degree of signal coupling between twoobjects, i.e., between pure “on” (coupled) and pure “off” (uncoupled)states, by the provision of one or more variable control signals.

SUMMARY

The capacitively-driven tunable coupler described herein leverages acoupling capacitor to connect an open end of a quantum object (i.e., anend of the object that cannot have a DC path to a low-voltage rail, suchas a ground node, without breaking the functionality of the object) toan RF SQUID having a Josephson element capable of providing variableinductance and therefore variable coupling to another quantum object.

One example provides a superconducting capacitively-driven tunablecoupler system that tunably couples and uncouples first and secondquantum objects each having a ground end required to be connected to aDC path to a low-voltage rail and an open end required not to beconnected to a DC path to the low-voltage rail. A coupler includes afirst coupling capacitor connected between the open end of the firstquantum object and a first connecting node, a radio-frequencysuperconducting quantum interference device (RF SQUID) connected betweenthe first connecting node and a second connecting node, the RF SQUIDcomprising a Josephson element connected between the first connectingnode and the second connecting node, and at least one flux injectionelement configured to bias the Josephson element to variably weaken thestrength of coupling between the first and second quantum objects.Injected flux can uncouple the objects and thereby isolate the objectsfrom exchanging signals between them. In the absence of injected flux,the objects are coupled together to pass signals between them.

In another example, a superconducting capacitively-driven tunablecoupler system tunably couples and uncouples first and second quantumobjects each having a ground end and an open end. The system includes acoupling capacitor connected between the open end of the first quantumobject and a first connecting node, a first inductor connected betweenthe first connecting node and the low-voltage rail, a Josephson elementconnected between the first connecting node and a second connectingnode, and a second inductor connected between the second connecting nodeand the low-voltage rail. The ground end of the second quantum object isconnected to the second connecting node.

In yet a further example, a superconducting capacitively-driven tunablecoupler system tunably couples and uncouples first and second quantumobjects each having a ground end and an open end. The system includes afirst coupling capacitor connected between the open end of the firstquantum object and a first connecting node, a first inductor connectedbetween the first connecting node and the low-voltage rail, a Josephsonelement connected between the first connecting node and a secondconnecting node, a second inductor connected between the secondconnecting node and the low-voltage rail, and a second couplingcapacitor connected between the second connecting node and the open endof the second quantum object.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an example superconductingcapacitively-driven tunable coupler.

FIG. 2A is a schematic circuit diagram of an example superconductingcapacitively-driven tunable coupler.

FIGS. 2B-2I are schematic diagrams illustrating various arrangementsproviding coupling of control flux to the example superconductingcapacitively-driven tunable coupler of FIG. 2A.

FIG. 3 is a schematic circuit diagram of an example superconductingcapacitively-driven tunable coupler having capacitive coupling at bothends of the coupler.

FIG. 4 is a schematic circuit diagram of an example superconductingcapacitively-driven tunable coupler having coupling on one side througha flux transformer.

DETAILED DESCRIPTION

This disclosure relates generally to superconducting circuits, and moreparticularly to a capacitively-driven tunable coupler between twoquantum objects (e.g. qubits or resonators). The applicability oftunable couplers that couple inductively is limited in certainsituations. For instance, a transmission line resonator has regionswhere the current flowing is essentially zero, while the voltageoscillations are at their maximum. Tunable couplers that coupleinductively are unable to couple at these points, because inductivecouplings only work where there is current flowing. Thus, for example,in the case of a half-wave resonator having one end shorted to alow-voltage rail (e.g., ground) and the other end left open, no currentflows at the open end, so while an inductive coupling may be made to theend shorted to ground and where there is current there to couple to, aninductive coupling cannot be made to the open end of the half-waveresonator.

The superconducting capacitively-driven tunable coupler described hereincan include a coupling capacitor and a radio-frequency superconductingquantum interference device (RF SQUID) to provide a tunable couplingelement that works where inductive couplings are unavailable. Thesuperconducting capacitively-driven tunable coupler described hereinprovides a tunable coupling element that can be driven capacitively by avoltage signal, rather than inductively by a current signal. Thesuperconducting coupler can operate at cryogenic temperatures, dissipatesubstantially no power, and can be controlled with single flux quantum(SFQ) compatible signals.

As shown in the block diagram of FIG. 1, a capacitively-driven tunablecoupler 102 couples a first quantum object 104 and a second quantumobject 106 connected to the coupler 102 via ports. Although these portshave been nominally labeled “IN” and “OUT” in FIG. 1 for simplicity ofdiscussion, the transmission of signals or exchange of informationbetween the coupled objects can be bidirectional. The quantum objects104, 106 can be qubits or resonators. One way to make a resonator of thetype contemplated is with a completely passive transmission line (i.e.,not a Josephson transmission line (JTL), which is active) with anappropriate choice of length and impedance. Coupler 102 consists of anRF SQUID 110 with a coupling capacitor 110 connected to one terminal ofthe RF SQUID 108 at connecting node 112. A Josephson element in the RFSQUID (not shown in FIG. 1) may be implemented, for example, as a singleJosephson junction or as a compound Josephson junction, comprising,e.g., two Josephson junctions in parallel.

One or more flux injection elements 114 can be provided to the coupler102, and specifically to its RF SQUID 108, to bias the RF SQUID 108 andthereby alter the inductance of the Josephson element in the RF SQUID108 to be switched between, on the one hand, a low inductance state forcoupling objects 104, 106 to one another and to pass signals between thecoupled objects 104, 106, and, on the other hand, a high inductancestate to decouple the objects from one another and thus to block signalsfrom passing between the decoupled objects.

A coupler controller 116 can control the setting of the coupler 102between an “off” (decoupled) state and various degrees of an “on”(coupled) state, by adjusting a Josephson element in RF SQUID 108between opposing inductance states. For example, the coupler controller116 can control an amount and polarity of control current through atleast one flux injection element 114, e.g., through at least one fluxbias control line inductively coupled to the RF SQUID 108.

FIG. 2A provides a circuit schematic of an example capacitively-driventunable coupler 200 that can correspond to coupler 102 in FIG. 1.Coupler 200 can couple first and second quantum objects 202, 204corresponding to objects 104, 106 in FIG. 1. First inductor L₁,Josephson junction J₁, and second inductor L₂ in coupler 200 form an RFSQUID that can correspond to RF SQUID 110 in FIG. 1. This RF SQUID formsan inductive current divider that is driven through coupling capacitorC₁, which can correspond to capacitor 110 in FIG. 1, by a voltage onfirst object 202. Node V₁, where coupling capacitor C₁ connects to theRF SQUID, can correspond to connecting node 112 in FIG. 1. For the sakeof simplicity, flux injection elements are omitted from FIG. 2A.However, flux can be injected in a variety of ways, several of which aredescribed herein and illustrated in FIGS. 2B-2I. First and secondobjects 202, 204 can be coupled with no flux applied via a controlcurrent, whereas a flux may be applied via one or more control currentsto decouple the objects 202, 204. In the discussion that follows, thevariable inductance of the Josephson element in the RQ SQUID (i.e., J₁in the example of FIG. 2A) will be referred to as L_(J).

In all of the examples described herein, first and second objects 202,204 can be each of a type having two unlike ends, wherein one end musthave a DC path to a low-voltage rail (e.g., ground), and one must nothave a DC path to the low-voltage rail. These will be referred to,respectively, as a ground end and an open end. The examples of FIGS.2A-2I can couple the open end of first object 202 (i.e., the end ofobject 202 that must not have a DC path to the low-voltage rail) to theground end of second object 204 (i.e., the end of second object 204 thatmust have a DC path to the low-voltage rail). Whereas coupling togetherground ends of objects 202, 204 (i.e., the ends of two objects that bothrequire a DC path to the low-voltage rail) can make use of a tunablecoupler that only couples inductively, such a coupler cannot be used tocouple, for either object, the open end (i.e., the end that must nothave a DC path to the low-voltage rail). In the instance where the openend of first object 202 is the end being coupled, replacing couplingcapacitor C₁ with a short circuit would break the functionality of firstobject 202, because the open end of first object 202 requires that therenot be a DC path to ground at that end.

The couplings and systems of the present disclosure make use of thediscovery that a current in a ground-L₁-L_(J)-L₂-ground loop that issufficient to result in a reasonable tunable coupling between the twoobjects can be achieved by placing an appropriately sized couplingcapacitor C₁ between first object 202 and node V₁. When the LC timeconstant of the series circuit formed by the coupling capacitor C₁ andthe rest of the coupler 200 is small compared to the drive frequency,the potential at node V₁ follows the potential on the first object 202.Current is thereby forced through the inductive divider formed by L₁ andthe sum of L₂ and L_(J). The branch current through L₂ is equal toL₁/(L₂+L_(J)), and second object 204 may then be coupled to this currenteither galvanically or through a flux transformer.

Inductance L_(J) of the Josephson element represented by singleJosephson junction J₁ in FIG. 2A depends on a control current biasingthe RF SQUID. For example, L_(J) can be varied by applying a flux biasto the RF SQUID loop, resulting in a tunable current through L₂ andtherefore a tunable coupling between the two objects 202, 204. Thevariable value of L_(J) thus sets the current in L₂ and hence thecoupling between first and second objects 202, 204. The values of thecapacitor C₁ and inductor L₁ should be chosen such that 1/√(L₁/C₁)<<ω,where ω represents the highest characteristic frequency of the coupledobjects 202, 204. Exact values for L₁ and C₁ are dependent on therequired coupling strength. Simulations performed in Agilent's AdvancedDesign Simulation (ADS) tool indicate that, for realistic choices of thecapacitance and inductance values, coupler 200 is able to achievereasonably strong couplings, on the order of 100 megahertz for a modelsystem.

The coupler described herein therefore provides the flexibility toimplement tunable couplings at any point along a transmission-lineresonator, to enable couplings not possible with tunable couplers thatonly couple inductively. The capacitively-driven tunable coupler system100 can be implemented in any of a variety of superconducting circuitsystems to provide coupling and decoupling between quantum objects(e.g., qubits, resonators). The signals between the coupled objects canbe, for example, microwave signals that are implemented in a controlscheme for a quantum circuit, such as performing a gate or a readoutoperation on a qubit. As another example, the signals can be a signalpulse, a communication signal, or a control command signal. Thecapacitively-driven tunable coupler system 100 can operate at cryogenictemperatures, can dissipate substantially no power, and can becontrolled with single flux quantum (SFQ) compatible signals.

As discussed above, the aforementioned Josephson elements in the RFSQUID of coupler 200 can be Josephson junctions or compound Josephsonjunctions. The inductance of the Josephson elements can be switchedbetween a low inductance state for coupling quantum objects to oneanother and to pass signals between the coupled objects, and a highinductance state to decouple the objects from one another to blocksignals from passing between the objects. The Josephson elements canhave a first inductance when no current or a low current is induced inits SQUID, and a second inductance when a current or a higher current isinduced in its respective SQUID that is at a predetermined thresholdthat generates or induces a flux, for example, greater than about 0.1 Φ₀and less than about 0.45 Φ₀, where Φ₀ is equal to a flux quantum. Thefirst inductance (e.g., ℏ/2e*1/I_(C), where ℏ is Planck's constantdivided by 2 π, e is electron charge, and I_(C) is the critical currentof the Josephson junction) can provide coupling between objects, such toallow passing of a desired bandwidth portion of an input signal betweenobjects. The second inductance (e.g., a comparatively large inductancevalue) can provide decoupling between the objects, such that the passingof the desired bandwidth portion of the input signal is blocked betweenobjects.

FIGS. 2B-2H illustrate schematic diagrams of couplers having variousarrangements for providing flux injection. The variant couplersotherwise function substantially as described above. Example coupler 206of FIG. 2B provides a single flux bias line 208 capable of providingflux injection by transformer-coupling into inductors L₁ and L₂. Examplecoupler 206 of FIG. 2B provides a single flux bias line 208 capable ofproviding flux injection by transformer-coupling into inductors L₁ andL₂. Example coupler 210 of FIG. 2C provides a single flux bias line 212capable of providing flux injection by transformer-coupling into justinductor L₁. Example coupler 214 of FIG. 2D provides a single flux biasline 216 capable of providing flux injection by transformer-couplinginto just inductor L₂. Example coupler 218 of FIG. 2E provides a firstflux bias line 220 capable of providing flux injection bytransformer-coupling into just inductor L₁ and a second flux bias line222 capable of providing flux injection by transformer-coupling intojust inductor L₂. Both flux bias lines 220, 222 could be controlled by asingle controller such as controller 116 in FIG. 1.

Example couplers 224, 230, 234, and 238 of FIGS. 2F-2I all provide theJosephson element of the RF SQUID as a compound Josephson junction 226consisting of two Josephson junctions J₁, J₂ arranged in parallel. Thesmaller loop of the compound Josephson junction 226 can also include oneor more inductors by which flux can be injected into the smaller loop.As illustrated in FIGS. 2F-2I, two such inductors, L_(A) and L_(B), areprovided in the compound Josephson junction 226. These inductors L_(A),L_(B) have comparatively small inductance values as compared to theinductance values of L₁ or L₂. Example coupler 224 of FIG. 2F provides asingle flux bias line 228 capable of providing flux injection intocompound Josephson junction 226 by transformer-coupling into justinductor L_(A). Example coupler 230 of FIG. 2G provides a single fluxbias line 232 capable of providing flux injection into compoundJosephson junction 226 by transformer-coupling into just inductor L_(B).Example coupler 234 of FIG. 2H provides a single flux bias line 236capable of providing flux injection into compound Josephson junction 226by transformer-coupling into both inductors L_(A) and L_(B). Examplecoupler 238 of FIG. 2I provides a first flux bias line 240 capable ofproviding flux injection by transformer-coupling into just inductorL_(A) and a second flux bias line 242 capable of providing fluxinjection by transformer-coupling into just inductor L_(B). Both fluxbias lines 240, 242 could be controlled by a single controller such ascontroller 116 in FIG. 1.

Whereas FIGS. 2A-2I illustrate capacitively-driven tunable couplers thatcan be used to couple the open end of first quantum object 202 to theground end of second quantum object 204, coupler 300 illustrated in FIG.3 can be used to couple the objects 302, 304 by the open ends of bothobjects. Coupler 300 behaves equivalently to the previously describedcouplers but further includes an additional coupling capacitor C₂connected on the other end of the RF SQUID at node V₂. Flux bias lines,for example, can be provided as flux injection elements in coupler 300in an equivalent manner as shown in any of FIGS. 2B-2I.

While FIGS. 2A-2I illustrate capacitively driven tunable couplers inwhich second quantum object 204 is galvanically coupled to the currentforced through the inductive divider formed by L₁ and the sum of L₂ andL_(J), FIG. 4 illustrates another example capacitively driven tunablecoupler in which second quantum object 404 is coupled to this current,and thus to first quantum object 402, through a flux transformer 408rather than a galvanic connection. Although the coupling control fluxline 406 is shown as arranged in the example of circuit 210 in FIG. 2C,the circuit 400 shown in FIG. 4 could also be modified to use thecontrol coupling arrangements 224 of FIG. 2F, 230 of FIG. 2G, 234 ofFIG. 2H, or 238 of FIG. 2I.

The capacitively-driven tunable coupler described herein provides theflexibility in systems having an extended object to couple to thatobject at more than just the ground end of the extended object. Thedescribed coupler permits the flexibility to couple at anywhere alongthe object.

What have been described above are examples of the invention. It is, ofcourse, not possible to describe every conceivable combination ofcomponents or methodologies for purposes of describing the invention,but one of ordinary skill in the art will recognize that many furthercombinations and permutations of the invention are possible.Accordingly, the invention is intended to embrace all such alterations,modifications, and variations that fall within the scope of thisapplication, including the appended claims. Additionally, where thedisclosure or claims recite “a,” “an,” “a first,” or “another” element,or the equivalent thereof, it should be interpreted to include one ormore than one such element, neither requiring nor excluding two or moresuch elements. As used herein, the term “includes” means includes butnot limited to, and the term “including” means including but not limitedto. The term “based on” means based at least in part on.

What is claimed is:
 1. A superconducting capacitively-driven tunablecoupler system comprising: first and second quantum objects each havinga ground end required to be connected to a DC path to a low-voltage railand an open end required not to be connected to a DC path to thelow-voltage rail; a coupler comprising: a first coupling capacitorconnected between the open end of the first quantum object and a firstconnecting node; a radio-frequency superconducting quantum interferencedevice (RF SQUID) connected between the first connecting node and asecond connecting node, the RF SQUID comprising a Josephson elementconnected between the first connecting node and the second connectingnode, wherein the entirety of a path between the first couplingcapacitor and the Josephson element is electrically short; and at leastone flux injection element configured to bias the Josephson element tovariably weaken the strength of coupling between the first and secondquantum objects, wherein the objects are coupled together to passsignals between them in the absence of injected flux.
 2. The system ofclaim 1, wherein the ground end of the second quantum object is coupledto the second connecting node either galvanically or through a fluxtransformer.
 3. The system of claim 1, further comprising a couplercontroller configured to control the setting of the coupler betweencoupled and uncoupled states by adjusting the amount of the injectedflux and thereby varying the inductance of the Josephson element.
 4. Thesystem of claim 3, wherein the coupler controller controls an amount andpolarity of current through at least one flux bias control lineinductively coupled to the RF SQUID.
 5. The system of claim 1, whereinthe RF SQUID further comprises a first inductor connected between thefirst connecting node and the low-voltage rail and a second inductorbetween the second connecting node and the low-voltage rail.
 6. Thesystem of claim 5, wherein the Josephson element consists of exactly oneJosephson junction.
 7. The system of claim 5, wherein the at least oneflux injection element is a flux bias line that is transformer-coupledto at least one of the first and second inductors.
 8. The system ofclaim 5, wherein the Josephson element comprises a compound Josephsonjunction comprising two Josephson junctions arranged in parallel.
 9. Thesystem of claim 8, wherein the at least one flux injection element is aflux bias line that is transformer-coupled to an inductance in thecompound Josephson junction.
 10. The system of claim 1, wherein thecoupler further comprises a second coupling capacitor connected betweenthe second connecting node and the open end of the second quantumobject.